2.1144   ODE No. 1144

\[ (3 a+b x) y'(x)+2 a x y''(x)+c y(x)=0 \]

✓ Mathematica : cpu = 0.0184172 (sec), leaf count = 88

DSolve[c*y[x] + (3*a + b*x)*Derivative[1][y][x] + 2*a*x*Derivative[2][y][x] == 0,y[x],x]
 

\[\left \{\left \{y(x)\to c_1 e^{-\frac {b x}{2 a}} U\left (-\frac {2 c-3 b}{2 b},\frac {3}{2},\frac {b x}{2 a}\right )+c_2 e^{-\frac {b x}{2 a}} L_{\frac {2 c-3 b}{2 b}}^{\frac {1}{2}}\left (\frac {b x}{2 a}\right )\right \}\right \}\]

✓ Maple : cpu = 0.15 (sec), leaf count = 60

dsolve(2*a*x*diff(diff(y(x),x),x)+(b*x+3*a)*diff(y(x),x)+y(x)*c=0,y(x))
 

\[y \left (x \right ) = {\mathrm e}^{-\frac {b x}{2 a}} \left (\operatorname {KummerM}\left (\frac {3 b -2 c}{2 b}, \frac {3}{2}, \frac {b x}{2 a}\right ) c_{1} +\operatorname {KummerU}\left (\frac {3 b -2 c}{2 b}, \frac {3}{2}, \frac {b x}{2 a}\right ) c_{2} \right )\]